Research On Unified Wall Function Of Hypersonic Turbulent Flow Based On Data Driven

Discovering governing equations from data is a major challenge in many fields of engineering and science;such as neuroscience,fluid mechanics,climate science and aerodynamics.These fields have abundant data,but the models are complex and uncertain.In fluid mechanics,when dealing with the turbulent boundary layer calculation problem,it is necessary to combine the wall function and the turbulence model to solve the turbulent boundary layer flow problem quickly and well.Wall functions are divided into standard wall functions and unified functions.The commonly used and recognized wall functions in theoretical calculations are Splading unified function,Nichols & Nelson unified function and Crocco-Busemann unified function.The three functions are quite different from the experimental results,and can only be used to observe the changing trend of physical quantities in the process of fluid flow,and they are of little significance in engineering.In engineering,standard wall functions are often used for experimental calculations,which will cause the problem of the temperature and velocity distribution discontinuity.In this paper,a unified wall function research suitable for engineering is carried out to address the above problems.With the rapid development of computer science and technology,the combination of turbulence models and machine learning algorithms has become popular,but there are fewer studies combining wall functions.This work combines machine learning algorithms with experimental wall mesh data,and uses machine learning algorithms to mine wall control equations from the wall data.Thesis based on the following three aspects to this objective.(1)A sparse representation algorithm based on elastic network optimization is proposed,combined with the merits of LASSO and Ridge regression to identify the data,and obtain the functional form directly from the data.This method designs candidate function items according to the independent variables,and uses an optimization algorithm based on elastic networks to solve the unknown coefficients of each function item,thereby obtaining the function form.(2)Apply the algorithm designed in(1)to the wall simulation data.The simulation data is produced by the numerical solution of the relevant wall function.Through the three wall function experiments of Splading,Nichols & Nelson,and Crocco-Busemann,it is found that the sparse representation algorithm designed in this work has lower complexity and higher accuracy than the LASSO algorithm.(3)Use the SMO algorithm to optimize the algorithm in(1),and then mine the experimental data of the wall grid to obtain a unified wall function suitable for engineering.The main dedication of this work is that the proposed sparse representation algorithm can accurately regress the model in simulation data with high accuracy.After the proposed algorithm is optimized using the SMO algorithm,it can dig out a unified wall function suitable for engineering from the experimental data of the wall grid,which provides help for further understanding of the engineering calculation of the turbulent boundary layer.